-
Multiominal Coefficients:
Distribute n people to m group with respectively sizes: n1,n2...,nm
Example: 4 people a,b,c,d => 2 groups, each group has 2 people:
- (ab)(cd)
- (ac)(bd)
- (ad)(bc)
- (bc)(ad)
- (bd)(ac)
- (cd)(ab)
Result:
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Number of vector (x1,x2..,xm) that:
is:
If
:
Example: If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible?:
x1+x2+x3+x4=8
if each school has to receive at least 1 blackboards:
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Number of vector (x1,x2..,xm) that:
with
-
Binomial coefficient:
-
Proposition 4.4
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In words, Proposition 4.4 states that the probability of the union of n events equals the sum of the probabilities of these events taken one at a time, minus the sum of the probabilities of these events taken two at a time, plus the sum of the probabilities of these events taken three at a time, and so on.